Singer-songwriter, very unwell, finding solace finally in country's capital (9)
I believe the answer is:
nashville
'country's capital' is the definition.
('capital' of country music)
'singer-songwriter very unwell finding solace finally' is the wordplay.
'singer-songwriter' becomes 'Nash' (Graham Nash of Crosby, Stills, and Nash).
'very' becomes 'v' (abbreviation).
'unwell' becomes 'ill' (similar in meaning).
'finding' means one lot of letters go next to another.
'finally' says to take the final letters.
The last letter of 'solace' is 'e'.
'nash'+'v'+'ill'+'e'='NASHVILLE'
'in' acts as a link.
(Other definitions for nashville that I've seen before include "country town" , "US city" , "Tennessee's capital" , "Grand Ole Opry city" , "Centre of country and western" .)